# How do you find the limit of #x^2 * e^x# as x approaches infinity?

The limit does not exist;

graph{(x^2)e^x [-10, 10, -5, 5]}

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To find the limit of x^2 * e^x as x approaches infinity, we can use L'Hôpital's rule. By applying this rule, we take the derivative of both the numerator and denominator separately and then evaluate the limit again.

Differentiating x^2 gives us 2x, and differentiating e^x gives us e^x.

Taking the limit again, we have (2x)/(e^x). As x approaches infinity, the numerator grows faster than the denominator, so the limit is infinity.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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